Two types of calculation processes have been distinguished in the literature: approximate processes are supposed to rely heavily on the non-verbal quantity system, whereas exact processes are assumed to crucially involve the verbal system. These two calculation processes were commonly distinguished by manipulation of two factors in addition…

Mastering single-digit arithmetic during school years is commonly thought to depend upon an increasing reliance on verbally memorized facts. An alternative model, however, posits that fluency in single-digit arithmetic might also be achieved via the increasing use of efficient calculation procedures. To test between these hypotheses, we used a…

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document "Improving Mathematics in Key Stages Two and Three" (Education Endowment Foundation, 2017). The review draws on a substantial parallel study by the same research team, funded by the Nuffield Foundation, which…

In decisions from experience, there are 2 experimental paradigms: sampling and repeated-choice. In the sampling paradigm, participants sample between 2 options as many times as they want (i.e., the stopping point is variable), observe the outcome with no real consequences each time, and finally select 1 of the 2 options that cause them to earn or…

This study investigated the role of strategy instruction and working memory capacity (WMC) on word problem solving accuracy in children with (n = 100) and without (n = 92) math difficulties (MD). Within classrooms, children in Grades 2 and 3 were randomly assigned to one of four treatment conditions: verbal-only strategies (e.g., underlining…

In this systematic review, we evaluated the evidence base of self-regulated strategy development (SRSD; Harris & Graham, 1992) for writing with students with and at risk for emotional or behavioral disorders (EBD). First, we evaluated the quality of studies identified (n 5 13) by applying the quality indicators for single case (Horner et al.,…

Numerical processing has been extensively studied by examining the performance on basic number processing tasks, such as number priming, number comparison, and number line estimation. These tasks assess the innate "number sense," which is assumed to be the breeding ground for later mathematics development. Indeed, several studies have…

The purpose of this study was to analyze how participants' levels of hemoglobin as they performed mathematics fluency and reading fluency (reading comprehension) compare. We used Optical Topography (OT, helmet type brain-scanning system, also known as Functional Near-Infrared Spectroscopy or fNIRS) to measure levels of brain activity. A central…

Specifying file references for hypertext links is an elementary competence that nevertheless draws upon core computational thinking concepts such as tree traversal and the distinction between relative and absolute references. In this article we explore the learning effects of different instructional strategies in the context of an introductory…

The relation between skill in simple addition and subtraction and more general math achievement in elementary school is well established but not understood. Both the intrinsic importance of skill in simple calculation for math and the influence of conceptual knowledge and cognitive factors (working memory, processing speed, oral language) on…

We report on results of a classroom teaching experiment in a mathematics content course for prospective elementary teachers. A local instruction theory for the development of number sense, which was previously applied to whole-number mental computation, was extended to inform instruction concerning reasoning about fraction magnitude. We found that…

Previous research suggests that perspective-taking and other "theory of mind" processes may be cognitively demanding for adult participants, and may be disrupted by concurrent performance of a secondary task. In the current study, a Level-1 visual perspective task was administered to 32 adults using a dual-task paradigm in which the secondary task…

We present a new software, called Goluca (Godinho, Luengo, and Casas, 2007), based on the technique of Pathfinder Associative Networks (Schvaneveldt, 1989), which produces graphical representations of the cognitive structure of individuals in a given field knowledge. In this case, we studied the strategies used by teachers and its relationship…

This study tested whether 10- and 12-year-olds who can correctly compare the magnitudes of fractions with common components access the magnitudes of the whole fractions rather than only compare the magnitudes of their components. Time for comparing two fractions was predicted by the numerical distance between the whole fractions, suggesting an…

Recently, Vul and Pashler (2008) demonstrated that the average of 2 responses from a single subject to general knowledge questions was more accurate than either single estimate. Importantly, this reveals that each guess contributes unique evidence relevant to the decision, contrary to views that eschew probabilistic representations of the…